WorldCat Identities

Stillwell, John

Works: 46 works in 330 publications in 3 languages and 9,566 library holdings
Genres: History  Textbooks  Conference papers and proceedings 
Roles: Author, Translator, Editor, tra, Contributor
Publication Timeline
Most widely held works by John Stillwell
Mathematics and its history by John Stillwell( Book )

72 editions published between 1989 and 2014 in English and German and held by 1,731 WorldCat member libraries worldwide

Recoge los cambios en esta ciencia desde el teorema de Pitágoras hasta la computación, incluyendo breves biografías de matemáticos eminentes y ejercicios
Numbers and geometry by John Stillwell( Book )

14 editions published between 1997 and 1998 in English and held by 872 WorldCat member libraries worldwide

Numbers and Geometry is a beautiful and relatively elementary account of a part of mathematics where three main fields - algebra, analysis, and geometry - meet. The aim of this book is to give a broad view of these subjects at the level of calculus, without being a calculus (or a pre-calculus) book. Its roots are in arithmetic and geometry, the two opposite poles of mathematics, and the source of historic conceptual conflict. The resolution of this conflict, and its role in the development of mathematics, is one of the main stories in the book. The key is algebra, which brings arithmetic and geometry together, and allows them to flourish and branch out in new directions
Elements of algebra : geometry, numbers, equations by John Stillwell( Book )

24 editions published between 1994 and 2010 in English and Italian and held by 816 WorldCat member libraries worldwide

This book is a concise, self-contained introduction to abstract algebra that stresses its unifying role in geometry and number theory. Classical results in these fields, such as the straightedge-and-compass constructions and their relation to Fermat primes, are used to motivate and illustrate algebraic techniques. Classical algebra itself is used to motivate the problem of solvability by radicals and its solution via Galois theory. This historical approach has at least two advantages: On the one hand it shows that abstract concepts have concrete roots, and on the other it demonstrates the power of new concepts to solve old problems
Roads to infinity : the mathematics of truth and proof by John Stillwell( Book )

14 editions published in 2010 in English and held by 665 WorldCat member libraries worldwide

Offers an introduction to modern ideas about infinity and their implications for mathematics. It unifies ideas from set theory and mathematical logic, and traces their effects on mainstream mathematical topics of today, such as number theory and combinatorics.--From publisher description
The four pillars of geometry by John Stillwell( Book )

4 editions published between 2005 and 2010 in English and held by 596 WorldCat member libraries worldwide

"The Four Pillars of Geometry approaches geometry in four different ways, devoting two chapters to each. This makes the subject accessible to readers of all mathematical tastes, from the visual to the algebraic. Not only does each approach offer a different view; the combination of viewpoints yields insights not available in most books at this level. For example, it is shown how algebra emerges from projective geometry, and how the hyperbolic plane emerges from the real projective line." "All readers are sure to find something new in this attractive text, which is abundantly supplemented with figures and exercises. This book will be useful for an undergraduate geometry course, a capstone course, or a course aimed at future high school teachers."--Résumé de l'éditeur
Yearning for the impossible : the surprising truths of mathematics by John Stillwell( Book )

18 editions published between 2006 and 2008 in English and held by 538 WorldCat member libraries worldwide

"This book explores the history of mathematics from the perspective of the creative tension between common sense and the "impossible" as the author follows the discovery or invention of new concepts that have marked mathematical progress: - Irrational and Imaginary Numbers - The Fourth Dimension - Curved Space - Infinity and others The author puts these creations into a broader context involving related "impossibilities" from art, literature, philosophy, and physics. By imbedding mathematics into a broader cultural context and through his clever and enthusiastic explication of mathematical ideas the author broadens the horizon of students beyond the narrow confines of rote memorization and engages those who are curious about the place of mathematics in our intellectual landscape."--Page ublisher description
Elements of number theory by John Stillwell( Book )

17 editions published between 2002 and 2010 in English and held by 430 WorldCat member libraries worldwide

"This book is a concise introduction to number theory and some related algebra, with an emphasis on solving equations in integers. Finding integer solutions led to two fundamental ideas of number theory in ancient times - the Euclidean algorithm and unique prime factorization - and in modern times to two fundamental ideas of algebra - rings and ideals." "The development of these ideas, and the transition from ancient to modern, is the main theme of the book. The historical development has been followed where it helps to motivate the introduction of new concepts, but modern proofs have been used where they are simpler, more natural, or more interesting. These include some that have not yet appeared in textbooks, such as a treatment of the Pell equation using Conway's theory of quadratic forms. Also, this is the only elementary number theory book that includes significant applications of ideal theory. It is clearly written, well illustrated, and supplied with carefully designed exercises, making it a pleasure to use as an undergraduate textbook or for independent study."--Jacket
Naive lie theory by John Stillwell( Book )

26 editions published between 2008 and 2012 in English and held by 334 WorldCat member libraries worldwide

Until recently, lie theory has been reserved for practictioners, with no lie theory for mathematical beginners. This book aims to fill that gap and it covers all the basics at a level appropriate for junior/senior level undergraduates
Papers on Fuchsian functions by Henri Poincaré( Book )

9 editions published in 1985 in English and German and held by 279 WorldCat member libraries worldwide

Mathematical evolutions( Book )

5 editions published in 2002 in English and held by 255 WorldCat member libraries worldwide

Elements of mathematics : from Euclid to Gödel by John Stillwell( Book )

11 editions published between 2016 and 2017 in English and held by 251 WorldCat member libraries worldwide

Elements of Mathematics takes readers on a fascinating tour that begins in elementary mathematics but, as John Stillwell shows, this subject is not as elementary or straightforward as one might think. Not all topics that are part of today's elementary mathematics were always considered as such, and great mathematical advances and discoveries had to occur in order for certain subjects to become "elementary." Stillwell examines elementary mathematics from a distinctive twenty-first-century viewpoint and describes not only the beauty and scope of the discipline, but also its limits. From Gaussian integers to propositional logic, Stillwell delves into arithmetic, computation, algebra, geometry, calculus, combinatorics, probability, and logic. He discusses how each area ties into more advanced topics to build mathematics as a whole. Through a rich collection of basic principles, vivid examples, and interesting problems, Stillwell demonstrates that elementary mathematics becomes advanced with the intervention of infinity. Infinity has been observed throughout mathematical history, but the recent development of "reverse mathematics" confirms that infinity is essential for proving well-known theorems, and helps to determine the nature, contours, and borders of elementary mathematics. Elements of Mathematics gives readers, from high school students to professional mathematicians, the highlights of elementary mathematics and glimpses of the parts of math beyond its boundaries
The real numbers : an introduction to set theory and analysis by John Stillwell( Book )

14 editions published between 2013 and 2017 in English and held by 146 WorldCat member libraries worldwide

While most texts on real analysis are content to assume the real numbers, or to treat them only briefly, this text makes a serious study of the real number system and the issues it brings to light. Analysis needs the real numbers to model the line, and to support the concepts of continuity and measure. But these seemingly simple requirements lead to deep issues of set theory"uncountability, the axiom of choice, and large cardinals. In fact, virtually all the concepts of infinite set theory are needed for a proper understanding of the real numbers, and hence of analysis itself. By focusing on the set-theoretic aspects of analysis, this text makes the best of two worlds: it combines a down-to-earth introduction to set theory with an exposition of the essence of analysis"the study of infinite processes on the real numbers. It is intended for senior undergraduates, but it will also be attractive to graduate students and professional mathematicians who, until now, have been content to "assume" the real numbers. Its prerequisites are calculus and basic mathematics. Mathematical history is woven into the text, explaining how the concepts of real number and infinity developed to meet the needs of analysis from ancient times to the late twentieth century. This rich presentation of history, along with a background of proofs, examples, exercises, and explanatory remarks, will help motivate the reader. The material covered includes classic topics from both set theory and real analysis courses, such as countable and uncountable sets, countable ordinals, the continuum problem, the Cantor-Schröder-Bernstein theorem, continuous functions, uniform convergence, Zorn's lemma, Borel sets, Baire functions, Lebesgue measure, and Riemann integrable functions
The four pillars of geometry by John Stillwell( Book )

20 editions published between 2005 and 2010 in English and Undetermined and held by 104 WorldCat member libraries worldwide

Demonstrates that geometry can be developed in four fundamentally different ways, and that all should be used if the subject is to be shown in all its splendour. Containing more than 100 figures, this book includes two chapters devoted to each approach, the first being concrete and introductory, while the second is more abstract
Wahrheit, Beweis, Unendlichkeit : eine mathematische Reise zu den vielseitigen Auswirkungen der Unendlichkeit by John Stillwell( Book )

6 editions published between 2013 and 2014 in German and held by 48 WorldCat member libraries worldwide

In dem Buch erkundet der preisgekrönte Autor John Stillwell die Konsequenzen, die sich ergeben, wenn man die Unendlichkeit akzeptiert, und diese Konsequenzen sind vielseitig und überraschend. Der Leser benötigt nur wenig über die Schulmathematik hinausgehendes Hintergrundwissen; es reicht die Bereitschaft, sich mit ungewohnten Ideen auseinanderzusetzen. Stillwell führt den Leser sanft in die technischen Details von Mengenlehre und Logik ein, indem jedes Kapitel einem einzigen Gedankengang folgt, der mit einer natürlichen mathematischen Frage beginnt und dann anhand einer Abfolge von historischen Antworten nachvollzogen wird. Auf diese Weise zeigt der Autor, wie jede Antwort ihrerseits zu neuen Fragen führt, aus denen wiederum neue Begriffe und Sätze entstehen. Jedes Kapitel endet mit einem Abschnitt "Historischer Hintergrund", der das Thema in den größeren Zusammenhang der Mathematik und ihrer Geschichte einordnet. Auf diese Weise werden zuerst die Schlüsselideen präsentiert, um sie anschließend aus einem größeren Blickwinkel nochmals zu zeigen und so zu vertiefen. Allerdings warten manche Leser vielleicht mit Ungeduld auf die Kernsätze; und diese Leser können, zumindest in einem ersten Durchgang die historischen Abschnitte überspringen. Andere, die von Anfang an am großen Bild interessiert sind, werden sich wiederum zunächst mit den historischen Hintergründen beschäftigen und erst anschließend die Details ergänzen. Das Buch zeigt, wie Mengenlehre und Logik sich gegenseitig befruchten und wie sie sich auf die Mainstream-Mathematik auszuwirken beginnen, wobei Letzteres eine jüngere Entwicklung darstellt, der noch nicht viel Raum in allgemein verständlichen Darstellungen gegeben worden ist. John Stillwell, ursprünglich aus Melbourne, Australien, stammend, ist Professor für Mathematik an der University of San Francisco. Sein Werk deckt ein großes Spektrum an Mathematik ab: Es reicht von Übersetzungen der Klassiker wie Dirichlet
Trees by Jean-Pierre Serre( Book )

7 editions published between 1980 and 2003 in English and Undetermined and held by 33 WorldCat member libraries worldwide

The present book is an English translation of "Arbres, Amalgames, SL(2)", published in 1977 by J-P. Serre, and written with the collaboration of H. Bass. The first chapter describes the "arboreal dictionary" between graphs of groups and group actions on trees. The second chapter gives applications to the Bruhat-Tits tree of SL(2) over a local field
Planning Support Systems and Smart Cities by Stan Geertman( )

7 editions published in 2015 in English and held by 21 WorldCat member libraries worldwide

This book is a selection of the best and peer-reviewed articles presented at the CUPUM (Computers in Urban Planning and Urban Management) conference, held in the second week of July 2015 at MIT in Boston, USA. The contributions provide state-of the art overview of the availability and application of Planning Support Systems (PSS) in the framework of Smart Cities
Surfaces and planar discontinuous groups by Heiner Zieschang( Book )

2 editions published in 1980 in English and held by 21 WorldCat member libraries worldwide

Reverse mathematics : proofs from the inside out by John Stillwell( Book )

4 editions published in 2018 in English and held by 11 WorldCat member libraries worldwide

"This book presents reverse mathematics to a general mathematical audience for the first time. Reverse mathematics is a new field that answers some old questions. In the two thousand years that mathematicians have been deriving theorems from axioms, it has often been asked: which axioms are needed to prove a given theorem? Only in the last two hundred years have some of these questions been answered, and only in the last forty years has a systematic approach been developed. In Reverse Mathematics, John Stillwell gives a representative view of this field, emphasizing basic analysis--finding the "right axioms" to prove fundamental theorems--and giving a novel approach to logic. Stillwell introduces reverse mathematics historically, describing the two developments that made reverse mathematics possible, both involving the idea of arithmetization. The first was the nineteenth-century project of arithmetizing analysis, which aimed to define all concepts of analysis in terms of natural numbers and sets of natural numbers. The second was the twentieth-century arithmetization of logic and computation. Thus arithmetic in some sense underlies analysis, logic, and computation. Reverse mathematics exploits this insight by viewing analysis as arithmetic extended by axioms about the existence of infinite sets. Remarkably, only a small number of axioms are needed for reverse mathematics, and, for each basic theorem of analysis, Stillwell finds the "right axiom" to prove it. By using a minimum of mathematical logic in a well-motivated way, Reverse Mathematics will engage advanced undergraduates and all mathematicians interested in the foundations of mathematics."--
Theory of algebraic integers by Richard Dedekind( Book )

7 editions published between 1996 and 2010 in English and held by 9 WorldCat member libraries worldwide

The invention of ideals by Dedekind in the 1870s was well ahead of its time, and proved to be the genesis of what today we would call algebraic number theory. His memoir 'Sur la Theorie des Nombres Entiers Algebriques' first appeared in instalments in the 'Bulletin des sciences mathematiques' in 1877. This is a translation of that work by John Stillwell, who also adds a detailed introduction that gives the historical background as well as outlining the mathematical obstructions that Dedekind was striving to overcome. Dedekind's memoir gives a candid account of his development of an elegant theory as well as providing blow-by-blow comments as he wrestled with the many difficulties encountered en route. A must for all number theorists
Ethnicity and integration by John C. H Stillwell( )

1 edition published in 2010 in English and held by 0 WorldCat member libraries worldwide

The theme of this volume is ethnicity and the implications for integration of our increasingly ethnically diversified population. New research findings from a range of census, survey and administrative data sources are presented, and case studies are included
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Numbers and geometry
Alternative Names
John Stillwell Australian mathematician

John Stillwell Australisch wiskundige

John Stillwell australischer Mathematiker

John Stillwell matemático australiano

John Stillwell mathématicien australien

Stillwell, J.

Stillwell, J. C. 1942-

Stillwell, J. (John)

Stillwell, John

Stillwell, John C.

Stillwell, John C. 1942-

Stillwell, John C. H.

Stillwell, John C. (John Colin)

Stillwell, John Colin 1942-

ג'ון סטילוול מתמטיקאי אוסטרלי

スティルウェル, J


English (271)

German (8)

Italian (1)

Numbers and geometryElements of algebra : geometry, numbers, equationsRoads to infinity : the mathematics of truth and proofThe four pillars of geometryYearning for the impossible : the surprising truths of mathematicsElements of number theoryNaive lie theoryPapers on Fuchsian functions